Layer diffusion, product

There are various theories on how passive films are formed however, there are two commonly accepted theories. One theory is called the oxide film theory and states that the passive film is a diffusion-barrier layer of reaction products (i.e., metal oxides or other compounds). The barriers separate the metal from the hostile environment and thereby slow the rate of reaction. Another theory is the adsorption theory of passivity. This states that the film is simply adsorbed gas that forms a barrier to diffusion of metal ions from the substrata. 

Accumulatory pressure measurements have been used to study the kinetics of more complicated reactions. In the low temperature decomposition of ammonium perchlorate, the rate measurements depend on the constancy of composition of the non-condensable components of the product mixture [120], The kinetics of the high temperature decomposition [ 59] of this compound have been studied by accumulatory pressure measurements in the presence of an inert gas to suppress sublimation of the solid reactant. Reversible dissociations are not, however, appropriately studied in a closed system, where product readsorption and diffusion effects within the product layer may control, or exert perceptible influence on, the rate of gas release [121]. 

This expression, the parabolic law [38,77,468], has been shown to be obeyed in the oxidation of metals, where the reactant is in the form of a thin sheet. Variations in behaviour are apparent when diffusion in the barrier layer is inhomogeneous as a consequence of cracking or due to the development of more than a single product layer. Alternative rate relations may be applicable, e.g. 

Komatsu [478] has put forward the hypothesis that reaction in many powder mixtures is initiated only at interparticle contact and that product formation occurs by diffusion through these contact zones. Here, one of the participating reactants is not covered with a coherent product layer. Quantitative consideration of this model leads to a modified Jander equation. 

Basu and Searcy [736] have applied the torsion—effusion and torsion— Langmuir techniques, referred to above for calcite decomposition [121], to the comparable reaction of BaC03, which had not been studied previously. The reaction rate at the (001) faces of single crystals was constant up to a product layer thickness of 1 mm. The magnitude of E (225.9 kJ mole-1) was appreciably less than the enthalpy of the reaction (252.1 kJ mole-1). This observation, unique for carbonates, led to the conclusion that the slowest step in BaC03 vacuum decomposition at 1160—1210 K is diffusion of one of the reaction components in a condensed phase or a surface reaction of C02 prior to desorption. 

While it is possible that surface defects may be preferentially involved in initial product formation, this has not been experimentally verified for most systems of interest. Such zones of preferred reactivity would, however, be of limited significance as they would soon be covered with the coherent product layer developed by reaction proceeding at all reactant surfaces. The higher temperatures usually employed in kinetic studies of diffusion-controlled reactions do not usually permit the measurements of rates of the initial adsorption and nucleation steps. 

The maintenance of product formation, after loss of direct contact between reactants by the interposition of a layer of product, requires the mobility of at least one component and rates are often controlled by diffusion of one or more reactant across the barrier constituted by the product layer. Reaction rates of such processes are characteristically strongly deceleratory since nucleation is effectively instantaneous and the rate of product formation is determined by bulk diffusion from one interface to another across a product zone of progressively increasing thickness. Rate measurements can be simplified by preparation of the reactant in a controlled geometric shape, such as pressing together flat discs at a common planar surface that then constitutes the initial reaction interface. Control by diffusion in one dimension results in obedience to the... 

Product layer diffusion Many fluid-solid reactions generate ash or oxide layers that impede further reaction. 

Diffusion through a product layer can be treated like a film resistance. The surface concentration is measured inside the ash layer at the unbumed surface of the particle. If the ash thickness is constant and as 0, then the rate has the form of Equation (11.48). The ash thickness will probably increase with time, and this will cause the rate constant applicable to a single particle to gradually decline with time. 

A parabolic rate law will also be obtained if part or even all, of the diffusion through the product layer is by grain boundary diffusion rather than diffusion through the volume of each grain. The volume diffusion coefficient is quite simply defined as the phenomenological coefficient in Fick s laws. The grain boundary diffusion must be described by a product, DbS, where S is the grain... 

An important difference between a shrinking particle reacting to form only gaseous product(s) and a constant-size particle reacting so that a product layer surrounds a shrinking core is that, in the former case, there is no product or ash layer, and hence no ash-layer diffusion resistance for A. Thus, only two rate processes, gas-film mass transfer of A, and reaction of A and B, need to be taken into account. 

These results take into account three possible processes in series mass transfer of fluid reactant A from bulk fluid to particle surface, diffusion of A through a reacted product layer to the unreacted (outer) core surface, and reaction with B at the core surface any one or two of these three processes may be rate-controlling. The SPM applies to particles of diminishing size, and is summarized similarly in equation 9.1-40 for a spherical particle. Because of the disappearance of the product into the fluid phase, the diffusion process present in the SCM does not occur in the SPM. 

The product layer progressively becomes thicker until the original reactants are completely consumed. These reactions involve two steps (i) the diffusion of reactants through the product layer and (ii) the reaction at the phase boundary. The relative rates of these steps determine the overall rate of reaction. 

If the transport process is rate-determining, the rate is controlled by the diffusion coefficient of the migrating species. There are several models that describe diffusion-controlled processes. A useful model has been proposed for a reaction occurring at the interface between two solid phases A and B [290]. This model can work for both solids and compressed liquids because it doesn t take into account the crystalline environment but only the diffusion coefficient. This model was initially developed for planar interface reactions, and then it was applied by lander [291] to powdered compacts. The starting point is the so-called parabolic law, describing the bulk-diffusion-controlled growth of a product layer in a unidirectional process, occurring on a planar interface where the reaction surface remains constant ... 

For ease of solution, it is assumed that the spherical shape of the pellet is maintained throughout reaction and that the densities of the solid product and solid reactant are equal. Adopting the pseudo-steady state hypothesis implies that the intrinsic chemical reaction rate is very much greater than diffusional processes in the product layer and consequently the reaction is confined to a gradually receding interface between reactant core and product ash. Under these circumstances, the problem can be formulated in terms of pseudo-steady state diffusion through the product layer. The conservation equation for this zone will simply reflect that (in the pseudo-steady state) there will be no net change in diffusive flux so... 

The parabolic-rate law for the growth of thick product layers on metals was first reported by Tammann (1920), and a theoretical interpretation in terms of ambipolar diffusion of reactants through the product layer was advanced later by Wagner (1936, 1975). Wagner s model can be described qualitatively as follows when a metal is... 

Let us systematize the possible boundary conditions for cation diffusion in a spinel. Since in the ternary system (at a given P and T) the chemical potentials of two components are independent, we may distinguish between three different transport situations. If A denotes a change across the product layer and O and AO are chosen as the independent components, the possibilities are... 

The bar over the diffusivity term indicates the product layer average. Ajuao is equal to the standard value of the formation Gibbs energy of the spinel, AGAB2oa. One finds from Eqn. (6.29) that the (parabolic) reaction rate constant (A 2 = 2-kt) is... 

Figure 10-3. Surface diffusion product of Co tracer on Fe,04 (110), as a function of the (relative) oxygen potential. T- 750°C [V. Stubican (1993)]. a = Segregation factor, <5 = width of surface layer. Insert bulk > . and D 0 in Fe,04 at T= 1200°C [R. Dieckmann, et al. (1978)].

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